Ask HN: Math books like SICP?

Post by zeta8 » Thu, Apr 17, 2014, 5:07 AM UTC

graycat wrote: post #80

jvreeland wrote: post #70

Earlier quoted context omitted.

Real Analysis by Royden is the source of my nightmares.

Royden is breathtakingly gorgeous. But, it can be good to skip some parts. The main content is just 'measure theory', and that's just freshman calculus grown up. Why? Because near 1900 it became clear that freshman calculus was clumsy for some important progress, especially cases of convergence of functions. Measure theory? Well, first cut, 'measure' is just a grown up version of ordinary area. Simple. Why interested…

I'd agree with your assessment of Royden. Another fantastic book on Lebesgue Integration/Measure theory is Lebesgue Integration in Euclidean Spaces by Frank Jones. Fantastic textbook.

Post by zeta8 » Thu, Apr 17, 2014, 5:14 AM UTC

I'm in a similar position as well - perhaps at just a wee bit higher level (am learning grad-level math by myself). Below is a list of books that I have enjoyed. Some might perhaps be at a slightly higher level than you might need right now though.

1. Analysis - The Elias Stein, Rami Shakarchi Analysis series, Meassure Theory by Terrence Tao, Lebesgue Integration on Euclidean Spaces by Frank Jones, A radical approach to Lebesgue Integration by Bressoud

2. Algebra - Can't do much better than the classic texts by Herstein & Artin here. I know Artin doesn't get much love but after a point, you really begin to appreciate it.

3. Complex Analysis - is there a better math book than Visual Complex Analysis by Needham?

4. Topology - i'm partial to a Dover book on Topology by Theodore Gamelin. I learnt the basics of point-set topology & homotopy form this book. Great exercises.

5. Number Theory - check out the 2 problem books on number theory by Ram Murty. Melvyn Nathanson's book is quite good as well.

6. Combinatorics - Combinatorics of Finite Sets by Ian Anderson. Extremal Combinatorics by Jukna.

7. Graph Theory - Diestel or Bondy/Murty.

8. Galois Theory - Rotman is great.

Re: Ask HN: Math books like SICP?

Re: Ask HN: Math books like SICP?